No matter whether you listen to audio books at home, driving to work, at the beach, or elsewhere, the format of your favorite is an important consideration. There are several options today which impact portability, cost, and long-term archival.
Cassette tapes were probably the first medium for distributing audio books, but they've long been obsoleted by digital recordings. If you still have old books on tape, you probably want to convert them as soon as possible. Casette tapes degrade with time, and new players are no longer made. The longer you wait, the less likely you'll be able to get a good transfer. You can convert your old tapes by connecting the headphones jack from the tape player to your computer's microphone jack with a 1/8" patch cord, starting the player and recording digitally.
Audio books on CD are one modern option, although they are being replaced by file formats such as MP3. CD-Digital Audio discs store sound digitally using an uncompressed format similar to WAV, AU, or AIFF. For voice recordings, the quality is excellent--undistinguishable from the original. But CDs themselves aren't very portable compared to modern MP3 players, and they only hold just under 80 minutes of audio each.
MP3 and other file formats playable with portable digital audio players are the most popular way to listen to audio books today. They have few disadvantages, and some small players can hold hundreds of hours of voice recordings. MP3 audio books are a very popular digital format, since all general-purpose digital audio players support them. Even though it is old as far as audio formats go, MP3 can still pack large amounts of voice efficiently without making an audible impact on quality. Since it's highly supported, it's a good format if you plan on archiving your purchased books.
There are a few file formats that are more modern than MP3 that you may want to consider as well. The MP4 audio format is the successor to MP3. It's also known as AAC (or HE-AAC) and is sometimes seen as a .M4A file. It's support is growing quickly, and it provides file savings compared to MP3 of around 10-40%. Some other options include the open-source Vorbis (OGG) format, lossless FLAC and ALAC, and formats designed specifically for speech, such as Speex and Opus (AKA CELT). While some of these offer even smaller filesizes for the same quality as more popular file formats, you may want to wait for them to become better supported before considering them as a storage format for your audiobook collection.